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A130469 Triangular array read by rows: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.

%I A130469 #3 Sep 08 2022 08:45:30
%S A130469 1,1,1,2,2,1,6,4,3,1,24,12,6,4,1,120,48,18,8,5,1,720,240,72,24,10,6,1,
%T A130469 5040,1440,360,96,30,12,7,1,40320,10080,2160,480,120,36,14,8,1,362880,
%U A130469 80640,15120,2880,600,144,42,16,9,1,3628800,725760,120960,20160,3600
%N A130469 Triangular array read by rows: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.
%C A130469 T is also defined in A129867, which gives row sums of T.
%e A130469 First seven rows of T are
%e A130469 [ 1 ]
%e A130469 [ 1, 1 ]
%e A130469 [ 2, 2, 1 ]
%e A130469 [ 6, 4, 3, 1 ]
%e A130469 [ 24, 12, 6, 4, 1 ]
%e A130469 [ 120, 48, 18, 8, 5, 1 ]
%e A130469 [ 720, 240, 72, 24, 10, 6, 1 ]
%o A130469 (Magma) m:=11; &cat[ [ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]: j in [1..m] ];
%Y A130469 Cf. A129867, A130470 (antidiagonal sums), A130471 (first differences of antidiagonal sums).
%K A130469 nonn,tabl
%O A130469 1,4
%A A130469 _Klaus Brockhaus_, May 28 2007